Finite Group Databasebeta

← #19146430

Subgroups — #19146430

Order 5504.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583589C211yesmaximal, characteristic, complemented
2#14583253C211yesmaximal, characteristic, complemented
3#14583227C211yesmaximal, characteristic, complemented
4#14583220C211yesmaximal, characteristic, complemented
5#14583199C211yesmaximal, characteristic, complemented
6#14583138C211yesmaximal, characteristic, complemented
7#14583126C211yesmaximal, characteristic, complemented
8#14583118C211yesmaximal, characteristic, complemented
9#14583061C211yesmaximal, characteristic, complemented
10#14583050C211yesmaximal, characteristic, complemented
11C4×#10621883C211yesmaximal, characteristic, complemented
12D4×C43⋊C8C211yesmaximal, characteristic, complemented
13#14582895C211yesmaximal, characteristic, complemented
14C2×#13063246C211yesmaximal, characteristic, complemented
15C43×#546C211yesmaximal, characteristic
16C2×#10621885C2211yescharacteristic, complemented
17C2×#10621883C2211yescharacteristic
18C2×#10621883C2211yescharacteristic
19C22×C43⋊C8C2211yescharacteristic
20C22×C43⋊C8C2211yescharacteristic, complemented
21#13063318—21no—
22#13063317C2211yescharacteristic, complemented
23#13063315—21no—
24#13063306—21no—
25#13063304C2211yescharacteristic
26#13063304C2211yescharacteristic, complemented
27C4×Dic86C2211yescharacteristic, complemented
28#13063284C2211yescharacteristic, complemented
29#13063281—21no—
30C2×C4⋊Dic43C2211yescharacteristic
31#13063258C2211yescharacteristic, complemented
32#13063256C2211yescharacteristic, complemented
33#13063256C2211yescharacteristic, complemented
34C4⋊(C43⋊C8)C2211yescharacteristic, complemented
35#13063249C2211yescharacteristic, complemented
36#13063249C2211yescharacteristic, complemented
37#13063249C2211yescharacteristic, complemented
38#13063248C2211yescharacteristic, complemented
39#13063246C2211yescharacteristic
40#13063246C2211yescharacteristic
41#13063246C2211yescharacteristic
42#13063246C2211yescharacteristic
43#13063246C2211yescharacteristic
44#13063246C2211yescharacteristic
45C22⋊(C43⋊C8)C2211yescharacteristic
46C22⋊(C43⋊C8)C2211yescharacteristic, complemented
47C4×C43⋊C8C2211yescharacteristic, complemented
48C2×#41×C43C2211yescharacteristic
49C22×D4×C43C2211yescharacteristic
50#124×C43C2211yescharacteristic
51#123×C43—21no—
52C22⋊Q8×C43C2211yescharacteristic
53#121×C43—21no—
54#121×C43C2211yescharacteristic
55#120×C43—21no—
56C4×D4×C43C2211yescharacteristic
57C4×D4×C43C2211yescharacteristic
58C2×C22⋊C4×C43—21no—
59C24×C43—21no—
60#41×C43—22no—
61#41×C43—41no—
62C2×Q8×C43C2311yescharacteristic
63C2×D4×C43—21no—
64C2×D4×C43—21no—
65C2×D4×C43—21no—
66C2×D4×C43—22no—
67C2×D4×C43—41no—
68C2×D4×C43D411yescharacteristic
69C2×D4×C43C2311yescharacteristic
70C2×D4×C43C2311yescharacteristic
71C22×C4×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43C2311yescharacteristic
74C22×C4×C43C2311yescharacteristic
75C22×Dic43—21no—
76C2×Dic86C2311yescharacteristic
77C4⋊C4×C43—21no—
78C4⋊C4×C43D411yescharacteristic
79C4⋊C4×C43C2311yescharacteristic
80C22⋊C4×C43—21no—
81C22⋊C4×C43—21no—
82C22⋊C4×C43—21no—
83C22⋊C4×C43—21no—
84C22⋊C4×C43—21no—
85C22⋊C4×C43D411yescharacteristic
86C22⋊C4×C43D411yescharacteristic
87C42×C43C2311yescharacteristic
88C22⋊Dic43—21no—
89C22⋊Dic43—21no—
90C22⋊Dic43—21no—
91#10621885—41no—
92#10621883—22no—
93#10621883—41no—
94C4⋊Dic43—21no—
95C4⋊Dic43C2311yescharacteristic
96C4⋊Dic43C2311yescharacteristic
97C4⋊Dic43C2311yescharacteristic
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103C4×Dic43—21no—
104C4×Dic43—21no—
105C2×C43⋊C8—41no—
106C2×C43⋊C8—41no—
107C2×C43⋊C8C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111C23×C43—21no—
112C23×C43—21no—
113C23×C43—42no—
114C23×C43—42no—
115C23×C43—81no—
116C23×C43C2×D411yescharacteristic
117C23×C43C2×D411yescharacteristic
118Q8×C43—21no—
119Q8×C43—21no—
120D4×C43—22no—
121D4×C43—21no—
122D4×C43—21no—
123D4×C43—21no—
124D4×C43—42no—
125D4×C43—42no—
126D4×C43—81no—
127D4×C43#4112yes—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—42no—
135C2×C4×C43—81no—
136C2×C4×C43C2×D411yescharacteristic
137C2×C4×C43C2×D411yescharacteristic
138C2×C4×C43C2×D411yescharacteristic
139C2×C4×C43C2×D411yescharacteristic
140C2×C4×C43C2411yescharacteristic
141C2×Dic43—21no—
142C2×Dic43—21no—
143C2×Dic43—21no—
144C2×Dic43—21no—
145C2×Dic43—42no—
146Dic86—21no—
147Dic86—21no—
148C43⋊C8—21no—
149C43⋊C8—21no—
150C43⋊C8—21no—
151C43⋊C8—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—22no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43—41no—
161C22×C43—41no—
162C22×C43—41no—
163C22×C43—84no—
164C22×C43#13512yes—
165C22×C43C22×D411yescharacteristic
166C4×C43—21no—
167C4×C43—21no—
168C4×C43—21no—
169C4×C43—21no—
170C4×C43—41no—
171C4×C43—41no—
172C4×C43C2×#4111yescharacteristic
173C4×C43H(5,𝔽2)11yescharacteristic
174Dic43—41no—
175Dic43—41no—
176Dic43—41no—
177Dic43—41no—
178#3296—431nomaximal, Sylow
179C2×C43—22no—
180C2×C43—41no—
181C2×C43—42no—
182C2×C43—81no—
183C2×C43#54611yescharacteristic
184C2×C43C2×#13511yescharacteristic
185C2×C43#57711yescharacteristic
186#552—431no—
187#546D4311yescharacteristic
188#488—431no—
189#483—431no—
190#482—431no—
191#478—431no—
192#467—431no—
193#465—431no—
194#464—431no—
195#452—431no—
196#450—431no—
197C4×SD16—431no—
198C8×D4—431no—
199#416—431no—
200C2×#102—431no—
201C43#329611yescharacteristic, complemented, Sylow
202C2×#41C2×D4311yescharacteristic
203C22×D4C2×D4311yescharacteristic
204C2×Q16—431no—
205C2×SD16—431no—
206C2×SD16—431no—
207C22×C8—431no—
208C22×C8—431no—
209#126—861no—
210#125—431no—
211#125—861no—
212#124C2×D4311yescharacteristic
213#123—21no—
214#123—861no—
215C22⋊Q8—431no—
216C22⋊Q8—431no—
217C22⋊Q8C2×D4311yescharacteristic
218#121—21no—
219#121C2×D4311yescharacteristic
220#120—21no—
221C4×Q8—431no—
222C4×D4C2×D4311yescharacteristic
223C4×D4C2×D4311yescharacteristic
224#117—431no—
225#117—861no—
226C2×C4⋊C4—431no—
227C2×C22⋊C4—21no—
228#107—431no—
229#106—431no—
230#106—431no—
231C4⋊C8—431no—
232#103—431no—
233#103—431no—
234#103—431no—
235#103—431no—
236#102—431no—
237#102—431no—
238#102—431no—
239#102—431no—
240#102—431no—
241#102—431no—
242C22⋊C8—431no—
243C22⋊C8—431no—
244C4×C8—431no—
245C24—21no—
246#41—22no—
247#41—41no—
248C2×Q8—431no—
249C2×Q8C22×D4311yescharacteristic
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—41no—
255C2×D4C22⋊D4311yescharacteristic
256C2×D4C22×D4311yescharacteristic
257C2×D4C22×D4311yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—861no—
261C22×C4C22×D4311yescharacteristic
262C22×C4C22×D4311yescharacteristic
263Q16—1721no—
264SD16—862no—
265SD16—1721no—
266C2×C8—431no—
267C2×C8—431no—
268C2×C8—431no—
269C2×C8—431no—
270C2×C8—1721no—
271C2×C8—1721no—
272C4⋊C4—21no—
273C4⋊C4—431no—
274C4⋊C4—431no—
275C4⋊C4—431no—
276C4⋊C4—861no—
277C4⋊C4—861no—
278C4⋊C4—861no—
279C4⋊C4—861no—
280C4⋊C4—861no—
281C4⋊C4—861no—
282C4⋊C4C22⋊D4311yescharacteristic
283C4⋊C4C22×D4311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—861no—
290C22⋊C4—861no—
291C22⋊C4—861no—
292C22⋊C4C22⋊D4311yescharacteristic
293C22⋊C4C22⋊D4311yescharacteristic
294C42—861no—
295C42—861no—
296C42C22×D4311yescharacteristic
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23C2×C22⋊D4311yescharacteristic
303C23C2×C22⋊D4311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—861no—
307Q8—861no—
308D4—22no—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—42no—
313D4—42no—
314D4—81no—
315D4#1062190012yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—81no—
324C2×C4—861no—
325C2×C4—861no—
326C2×C4—861no—
327C2×C4—861no—
328C2×C4—1722no—
329C2×C4C2×C22⋊D4311yescharacteristic
330C2×C4C2×C22⋊D4311yescharacteristic
331C2×C4C2×C22⋊D4311yescharacteristic
332C2×C4C2×C22⋊D4311yescharacteristic
333C2×C4C23×D4311yescharacteristic
334C8—861no—
335C8—861no—
336C8—861no—
337C8—861no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—22no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—84no—
350C22#1306334512yes—
351C22C22×C22⋊D4311yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—1721no—
359C4—1721no—
360C4—1721no—
361C4—1721no—
362C4C2×#1062190011yescharacteristic
363C4#1306337011yescharacteristic
364C2—22no—
365C2—41no—
366C2—42no—
367C2—81no—
368C2#1458354311yescharacteristic
369C2C2×#1306334511yescharacteristic
370C2#1458371011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#546C2
socleC22×C43C22×D4
hypercenter#546D43
hypocenterC43#3296
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #14583589C2semidirect
2. #14583253C2semidirect
3. #14583227C2semidirect
4. #14583220C2semidirect
5. #14583199C2semidirect
6. #14583138C2semidirect
7. #14583126C2semidirect
8. #14583118C2semidirect
9. #14583061C2semidirect
10. #14583050C2semidirect
11. C4×#10621883C2semidirect
12. D4×C43⋊C8C2semidirect
13. #14582895C2semidirect
14. C2×#13063246C2semidirect
16. C2×#10621885C22semidirect
20. C22×C43⋊C8C22semidirect
22. #13063317C22semidirect
26. #13063304C22semidirect
27. C4×Dic86C22semidirect
28. #13063284C22semidirect
31. #13063258C22semidirect
32. #13063256C22semidirect
33. #13063256C22semidirect
34. C4⋊(C43⋊C8)C22semidirect
35. #13063249C22semidirect
36. #13063249C22semidirect
37. #13063249C22semidirect
38. #13063248C22semidirect
46. C22⋊(C43⋊C8)C22semidirect
47. C4×C43⋊C8C22semidirect
201. C43#3296semidirect